1. Field of the Invention
The present invention relates to curve generation technology in the designs of shapes, especially the designs of curved surfaces, employing computers in mechanical CAD, CG, etc.
2. Related Art
Heretofore, a curve display method employing a computer has displayed a curve by a line approximation wherein parameter values of equal intervals or ones of unequal intervals dependent upon the curving condition (or curvature) of the curve are put in a function expressive of the curve so as to generate a plurality of points, which are thereafter connected with straight lines. Regarding a method of displaying the feature quantity of a curve, the curving condition of the curve is usually displayed by drawing and displaying tangential vectors, normal vectors, curvature vectors, radius-of-curvature vectors, or the like which extend from arbitrary points on a planar curve displayed on a display screen. As a known example, an evaluation technique for the smoothness of a curve utilizing a curvature distribution (here, the arrangement of radius-of-curvature vectors in a queue along the curve) is disclosed in "Masatake Higashi et al: New CAD System for Style Design of an Outer Shape of a Car Body" contained in `Toyota Gijutsu`, Vol. 33, No. 2, 1983.
Another curve display method of the relevant type is disclosed in the official gazette of Japanese Patent Application Laid-open (KOKAI) No. 93880/1990.
In expressing a curve (termed "planar curve") which exists on a plane (section), even the polygonal line approximation display as in the prior-art method suffices. However, in a case where a three-dimensional curve (also termed "three-dimensional space curve") is to be displayed on a two-dimensional display screen, shape information in a depthwise direction (in a direction perpendicular to the display screen) cannot be expressed. Further, with the method as in the prior art wherein the radius-of-curvature vectors are queued and displayed along the three-dimensional space curve as the feature quantity of the curve, the torsion of the curve cannot be expressed for the following reason: Unlike that of the planar curve, the normal vector or the radius-of-curvature vector of the three-dimensional space curve sometimes has a component in the depthwise direction. In such a case, the magnitude of the true vector is not seen on the two-dimensional display screen, but the magnitude of the vector projected on the display screen is seen.